How to calculate (simple) historical volatlity

Historical daily volatility is the square root of the daily variance estimate. If we assume 1. mean return = 0 and 2. MLE rather than unbiased estimate, then daily variance is AVERAGE SQUARED RETURN

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Education

Tags:

• frm
• risk
• volatility

[hecathepeca]

Hi! Nice and educational videos. However, in this particular video at 4:38 I think you made a mistake. The volatility and variance are time averages, so there is no point in "applying the square root rule". If the process stays (statistically) the same over the whole year, then the volatility stays the same too. Here you're basically assuming that the volatility increases over time! The average square of a brownian motion does grow linearly in time, so I think you confused the "rule" with that.

[bionicturtledotcom]

@hecathepeca Thanks but wrong. I am not assuming volatility increases over time. It's periodicity. We retrieve a DAILY volatility and then, sometimes, want to express the same volatility in per annum (i.e., annualized). We can't here access a per annum vol directly (as an input, it's given in per annum); even if we had 252 days, we'd only use 2 endpoints. If returns are i.i.d., per annum vol = daily vol * SQRT(T/1) where T = trade days/year.

[bionicturtledotcom]

@hecathepeca The "square root rule" merely translates volatility periodicity (e.g., daily to annual; daily to 3-year; annual to daily), it's the SQRT(T) in BSM (assisting in rigorous assumption that vol is constant). Often used, and convenient, but also unrealistic as it assumes i.i.d. (stable) returns distribution. But we use it a lot b/c many finance problems express the volatility (i.e., annualized standard deviation) as XX% per annum.

[glenhojer]

The average is assumed constant at 0, so why call it a moving average?

Maybe if you used a MA(q) process, then it might be okay to call it a MA volatility, but still why not just call it volatility, it's shorter, more fitting?

and why show howto calculate the wrong st.dev. when it is easy in excel to calculate the right one using either =stdev() or =stdevp().

[bionicturtledotcom]

Hi glen, 1. MA refers to the trailing window (in this case, average of last 20); MA reminds of abrupt "ghosting" drop-off as move forward; 2. "volatility" includes dozens of schemes; 3. Right, you sure can use STDEV(), as suggested, that's more precise; but the above is more common b/c it is more tractable as we generalize to EWMA & GARCH

[hecathepeca]

@bionicturtledotcom yeah my mistake, I didn't read the definition carefully enough...

[cimao75]

Dear bionicturtle,

I consider you video series wonderful source of education! Thanks for the great job!

Nevertheless I found an interesting issue with continuous compounding during my assessment of a financial data series, on which I would like to get your opinion. While calculating positive cont. comp. returns it all seams OK, but what about the following situation:

LN (100/300) = -109,86%

How can this be justified mathematically.

Will appreciate your comment on this.

Thanks!

[gutrp]

Good informative video!

Its actually helpful for people who do credit spreads (I sometimes do).

Suppose If I want to know how far the stock could go up or down tomorrow (say), Is ATR better or the historical volatility data better? If so why? I would like to know your opinion.